1.3. Consolidated-undrained test (CU test)

For consolidated-undrained tests, at failure, Major Principal total stress =σ3=Δσf=σ1 Minor principal total stress =σ3

In consolidated-undrained tests, the conditions for stress are defined during the test. The major principal total stress represents the stress experienced by the sample at failure, which is the point where the sample can no longer withstand the load. The formula indicates that at this point, the major principal total stress (σ1) equals the confining pressure (σ3) plus the change in stress (Δσf). At the same time, the minor principal total stress remains equal to the confining pressure (σ3), meaning it does not change despite the introduction of additional stress.

Imagine trying to push down on a sponge that is already being squeezed in a container filled with water. The container’s pressure (σ3) is keeping the sponge from expanding, while your push is an added stress (Δσf). When you reach the point where the sponge compresses fully and can't take any more force, that's like reaching the failure point of the soil in a CU test. The internal pressure holding the sponge limits how much more pressure it can take from above.

Major principal effective stress =(σ3+Δσf)−uf=σ′1 Under Revision Minor principal effective stress =σ3− uf=σ′3

In a CU test, understanding effective stresses is critical. Effective stress refers to the stress that contributes to the actual mechanical strength of the soil. For the major principal effective stress (σ′1), we deduct the pore water pressure (uf) from the total stress, which gives a clearer picture of how the soil will behave under load. The minor principal effective stress is similarly deduced from the total stress by the same pore water pressure. This distinction is crucial in geotechnical engineering as it influences the stability and load-bearing capacity of soil structures.

Think of effective stress like a balloon filled with water. If you push down on the balloon, the pressure inside increases, but only a part of that pressure helps the balloon maintain its shape (the effective stress). The water within adds pressure but doesn't hold up the shape; if the balloon leaks, more pressure is needed from your push to keep it intact. The strength of the soil, like the integrity of the balloon, comes not just from the applied stress, but how much of that stress is 'effective' in resisting deformation.

The total stress Mohr’s circles at failure can now be plotted, as shown in figure, and then a common tangent can be drawn to define the failure envelope. This total stress failure envelope is defined by the equation s=ccu+σtanϕcu Where ccu and ϕcu are the consolidated-undrained cohesion and angle of friction respectively (Note: ccu≈0 for normally consolidated clays)

In CU tests, plotting Mohr’s circles helps visualize stress states. The total stress failure envelope, represented by the equation, illustrates how the shear stress (s) is related to the cohesive strength (ccu) of the soil and its angle of internal friction (ϕcu). A tangent line drawn through the plotted stress points indicates the maximum shear stress the soil can withstand before failure, providing critical information for engineering applications.

Imagine balancing a book on top of another book. The upper book can only be supported up to a point before it slips. The tangled interaction of the books represents the different stress states. The maximum angle at which they can stay balanced before sliding off is like the failure envelope; if you exceed this angle, the books fail to maintain balance, much like how soil fails under excessive stress.

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